It depends which country you want to teaching, and what sort of school.
But generally, for many Asian/S. American countries, and English-speaking passport and a degree i anything is enough.
Some also like some form of teaching qualification.

Specialist ESL, etc training will open a few more jobs and a handful more countries, but for individual requirements see the country-specific forums on eslcafe.

If you want to work in an International School (a school in, say, Tokyo, for ex-pat kids, using the British/American high school curriculum), you'd need to be Secondary-qualified.
If you wanted to work in a developed country's Uni then you might need an MA TESOL. But generally not in Asia/S. America.